Add normalization options for FFT (#146)

* Add normalization options for FFT

* Harmonize function signatures

fastmri/fftc.py

@@ -14,58 +14,70 @@
     import torch.fft  # type: ignore
 
 
-def fft2c_old(data: torch.Tensor) -> torch.Tensor:
+def fft2c_old(data: torch.Tensor, norm: str = "ortho") -> torch.Tensor:
     """
     Apply centered 2 dimensional Fast Fourier Transform.
 
     Args:
         data: Complex valued input data containing at least 3 dimensions:
             dimensions -3 & -2 are spatial dimensions and dimension -1 has size
             2. All other dimensions are assumed to be batch dimensions.
+        norm: Whether to include normalization. Must be one of ``"backward"``
+            or ``"ortho"``. See ``torch.fft.fft`` on PyTorch 1.9.0 for details.
 
     Returns:
         The FFT of the input.
     """
     if not data.shape[-1] == 2:
         raise ValueError("Tensor does not have separate complex dim.")
+    if norm not in ("ortho", "backward"):
+        raise ValueError("norm must be 'ortho' or 'backward'.")
+    normalized = True if norm == "ortho" else False
 
     data = ifftshift(data, dim=[-3, -2])
-    data = torch.fft(data, 2, normalized=True)
+    data = torch.fft(data, 2, normalized=normalized)
     data = fftshift(data, dim=[-3, -2])
 
     return data
 
 
-def ifft2c_old(data: torch.Tensor) -> torch.Tensor:
+def ifft2c_old(data: torch.Tensor, norm: str = "ortho") -> torch.Tensor:
     """
     Apply centered 2-dimensional Inverse Fast Fourier Transform.
 
     Args:
         data: Complex valued input data containing at least 3 dimensions:
             dimensions -3 & -2 are spatial dimensions and dimension -1 has size
             2. All other dimensions are assumed to be batch dimensions.
+        norm: Whether to include normalization. Must be one of ``"backward"``
+            or ``"ortho"``. See ``torch.fft.ifft`` on PyTorch 1.9.0 for
+            details.
 
     Returns:
         The IFFT of the input.
     """
     if not data.shape[-1] == 2:
         raise ValueError("Tensor does not have separate complex dim.")
+    if norm not in ("ortho", "backward"):
+        raise ValueError("norm must be 'ortho' or 'backward'.")
+    normalized = True if norm == "ortho" else False
 
     data = ifftshift(data, dim=[-3, -2])
-    data = torch.ifft(data, 2, normalized=True)
+    data = torch.ifft(data, 2, normalized=normalized)
     data = fftshift(data, dim=[-3, -2])
 
     return data
 
 
-def fft2c_new(data: torch.Tensor) -> torch.Tensor:
+def fft2c_new(data: torch.Tensor, norm: str = "ortho") -> torch.Tensor:
     """
     Apply centered 2 dimensional Fast Fourier Transform.
 
     Args:
         data: Complex valued input data containing at least 3 dimensions:
             dimensions -3 & -2 are spatial dimensions and dimension -1 has size
             2. All other dimensions are assumed to be batch dimensions.
+        norm: Normalization mode. See ``torch.fft.fft``.
 
     Returns:
         The FFT of the input.
@@ -76,22 +88,23 @@ def fft2c_new(data: torch.Tensor) -> torch.Tensor:
     data = ifftshift(data, dim=[-3, -2])
     data = torch.view_as_real(
         torch.fft.fftn(  # type: ignore
-            torch.view_as_complex(data), dim=(-2, -1), norm="ortho"
+            torch.view_as_complex(data), dim=(-2, -1), norm=norm
         )
     )
     data = fftshift(data, dim=[-3, -2])
 
     return data
 
 
-def ifft2c_new(data: torch.Tensor) -> torch.Tensor:
+def ifft2c_new(data: torch.Tensor, norm: str = "ortho") -> torch.Tensor:
     """
     Apply centered 2-dimensional Inverse Fast Fourier Transform.
 
     Args:
         data: Complex valued input data containing at least 3 dimensions:
             dimensions -3 & -2 are spatial dimensions and dimension -1 has size
             2. All other dimensions are assumed to be batch dimensions.
+        norm: Normalization mode. See ``torch.fft.ifft``.
 
     Returns:
         The IFFT of the input.
@@ -102,7 +115,7 @@ def ifft2c_new(data: torch.Tensor) -> torch.Tensor:
     data = ifftshift(data, dim=[-3, -2])
     data = torch.view_as_real(
         torch.fft.ifftn(  # type: ignore
-            torch.view_as_complex(data), dim=(-2, -1), norm="ortho"
+            torch.view_as_complex(data), dim=(-2, -1), norm=norm
         )
     )
     data = fftshift(data, dim=[-3, -2])